Question

We want to determine the strength of the relationship between the independent variable "age" and the dependent variable "intelligence quotient". In our sample, the mean of the variable "age" is equal to 14, and its variance is equal to 46,4. The mean of the variable "intelligence quotient" is equal to 102, and its variance is equal to 0. The list of corresponding data for the two variables is pictured below.

Determine the value of the correlation coefficient between the two variables.

a) -1

b) 0

c) 0,66

d) 1,25

e) none of the above

Ladividual. Age 1Q 22 | 102 18 | 102 14 | 102 16 | 102 2 | 102 12 | 102 |րում |ք|C

Answer 1

the value of the correlation coefficient between the two variables is:-

none of the above.

[explanation:-

given data are:-

$\bar{x}=14,\bar{y}=102,s_{x}^2=46.4,s_{y}^2=0$

x	y	$(x-\bar{x})*(y-\bar{y})$
22	102	0
18	102	0
14	102	0
16	102	0
2	102	0
12	102	0
		sum=0

$r=\frac{cov(x,y)}{s_{x}s_{y}}=\frac{\frac{1}{n-1}*\sum (x-\bar{x})(y-\bar{y})}{\sqrt{s_{x}^2*s_{y}^2}}=\frac{0}{\sqrt{46.4*0}}=not \ defined$]

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